Some Theory for Random Fields - With applications to Geostatistics: MSc. thesis written by Philipp Pluch (Klagenfurt University) under the supervision of J. Pilz (Klagenfurt University) and W. Mueller (Linz University). In this thesis the author tries to give an overview of the current used Bayesian methods in spatial prediction theory based on the assumption of an a-priori distribution of the unknown trend parameter and he tried to extend them to second moments based on the covariance parameter. After a functional analytic approach for random fields the concept if BLUPs are considered and discussed, methods of interpolation by splines and pde's are discussed by practical examples. A main result is a fully Bayesian approach for the predictive density -which is shown throw a practical example.